ClusterVQE algorithm offers quantum parallel approach for quantum chemistry simulations

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Schematic diagram of ClusterVQE algorithm. To simulate a molecule with 2N spin orbitals, VQE uses a quantum circuit defined on 2N qubits. In contrast, ClusterVQE splits the original 2N-qubit circuit into 2 N-qubit circuits by removing the entanglement between them via a dressed Hamiltonian.

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Quantum computers are inherently perfect platforms for simulating molecules, as recognized by Los Alamos National Laboratory researcher Richard Feynman in the 1980s. A flagship algorithm for quantum chemistry, the variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenstates of a given Hamiltonian on noisy intermediate-scale quantum (NISQ) devices. However, existing NISQ devices have a limited number of qubits and short circuit depth, two significant impediments to applying quantum algorithms like the VQE to realistic molecular systems.  

In new research published in the journal npj Quantum Information, researchers from Los Alamos National Laboratory propose a “ClusterVQE” algorithm. The ClusterVQE algorithm divides the simulation of larger molecules into smaller clusters so that each cluster can separately be solved on small quantum devices — the quantum counterpart of classical parallel computation. It is the first time that both circuit depth and circuit width (the number of qubits) are simultaneously reduced.

Simulating molecular properties accurately from the first principles is fundamentally challenging because the computational cost increases factorially against the system size and accuracy. The complexity of quantum circuits imposes limits on their practical realization for problems like molecular simulations. In contrast, quantum computers may significantly reduce computational scaling by leveraging quantum systems as processors. The ClusterVQE algorithm reduces quantum circuit complexity in VQE for electronic structure calculations. The initial qubit space is split into clusters, which are further distributed on individual (shallower) quantum circuits. The clusters are obtained based on mutual information reflecting maximal entanglement between qubits, whereas inter-cluster correlation is taken into account via a new, dressed Hamiltonian. ClusterVQE therefore allows exact simulation of the problem by using fewer qubits and shallower circuit depths at the cost of additional classical resources, making it a potential leader for quantum chemistry simulations on NISQ devices. The research team has presented proof-of-principle demonstrations for several molecular systems based on quantum simulators as well as IBM quantum devices.

The research team’s work provides a practical and quantum parallel scheme for situating large molecules on small quantum devices, which significantly reduces the quantum resource requirements. The ClusterVQE algorithm likely paves the way toward reaching quantum chemistry advantage on NISQ devices.

Funding and mission

The work was supported by the Laboratory Directed Research and Development program. The work supports the Global Security mission area and the Information, Science and Technology capability pillar.

Reference

“Variational Quantum Eigensolver with Reduced Circuit Complexity,” npj Quantum Information, 8, 96 (2022); DOI: 10.1038/s41534-022-00599-z. Authors: Yu Zhang, Lukasz Cincio, Christian F.A. Negre, Piotr Czarnik, Patrick J. Coles, Petr M. Anisimov, Susan M. Mniszewski, Sergei Tretiak and A. Pavel Dub (Los Alamos National Laboratory).

Technical Contact: Yu Zhang (T-1)